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None of the conclusions drawn from this plot is significantly dependent on the actual set of nodels adopted (see. for example. Fig. 13.. | None of the conclusions drawn from this plot is significantly dependent on the actual set of models adopted (see, for example, Fig. \ref{mgbuzz}, |
below). | below). |
In the lower panel of Fig. | In the lower panel of Fig. |
12 the same diagram is shown for the Galactic GCs. | \ref{HbMg2} the same diagram is shown for the Galactic GCs. |
The H8 and Mg?indices are taken from GO9. | The $\beta$ and Mg2indices are taken from G09. |
In this case we classified as BHB clusters with wet>0.0 and as RHB those with p24.< 0.0. where the values of the classical HB morphology v are taken fromHarris (1996)). | In this case we classified as BHB clusters with $\frac{B-R}{B+R+V}>0.0$ and as RHB those with $\frac{B-R}{B+R+V}<0.0$ , where the values of the classical HB morphology $\frac{B-R}{B+R+V}$ are taken fromHarris \cite{harris}) ). |
evolution parameter for both ry and. ny. | evolution parameter for both $r_{0}$ and $n_{0}$. |
Our mocdel is therefore specified by four parameters: 7. 7g. 0 and zi | Our model is therefore specified by four parameters: $\tau_{g}$ , $\tau_{B}$, $\delta$ and $z_{dust}$. |
Our calculations assume a combination of values for the parameters (7,. rg) and (9. tac) that bracket the range consistent with existing observations. | Our calculations assume a combination of values for the parameters $\tau_{g}$, $\tau_{B}$ ) and $\delta$, $z_{dust}$ ) that bracket the range consistent with existing observations. |
“Phe values (74. τη) are chosen from. previous studies of dust. distributions and extinction in nearby spirals. | The values $\tau_{g}$, $\tau_{B}$ ) are chosen from previous studies of dust distributions and extinction in nearby spirals. |
From the studies of Giovanelli et al. ( | From the studies of Giovanelli et al. ( |
1994) and Disney DPhillipps (1995) (see also references therein) we assume the range in central optical depths: O.587rest. while dust scale radii of 5z(ro/kpc)z30 are assumed from Zaritsky (1994) and Peleticr et al. ( | 1994) and Disney Phillipps (1995) (see also references therein) we assume the range in central optical depths: $0.5\simlt\tau_{B}\simlt4$, while dust scale radii of $5\simlt (r_{0}/{\rm kpc})\simlt30$ are assumed from Zaritsky (1994) and Peletier et al. ( |
1€995). | 1995). |
For a nominal comoving galactic density of my=0.00277,Mpc.7 (eg. | For a nominal comoving galactic density of $n_{0}=0.002h_{50}^{3}{\rm Mpc^{-3}}$ (eg. |
Efstathiou et al. | Efstathiou et al. |
1988). these scale radii correspond. to a range for 7, (equation. 10)): 0.01zz,0.18. | 1988), these scale radii correspond to a range for $\tau_{g}$ (equation \ref{tg2}) ): $0.01\simlt\tau_{g}\simlt0.18$. |
These ranges are consistent with those assumedin the intervening galaxy obscuration mocdels of Leister Ostriker (1988) and Fall Pei (1993). | These ranges are consistent with those assumedin the intervening galaxy obscuration models of Heisler Ostriker (1988) and Fall Pei (1993). |
The values for (9. τμ) were chosen to cover a range of evolution strengths for ry and 7g respectively. | The values for $\delta$, $z_{dust}$ ) were chosen to cover a range of evolution strengths for $r_{0}$ and $\tau_{B}$ respectively. |
To cover a plausible range of dust. formation epochs. we consider 6ποunenC20. consistent with a range of galaxy ‘formation’ epochs predicted by existing theories of structure formation (eg. | To cover a plausible range of dust formation epochs, we consider $6\leq z_{dust}\leq20$, consistent with a range of galaxy `formation' epochs predicted by existing theories of structure formation (eg. |
Peebles 1989). | Peebles 1989). |
Ehe upper bound τω=20 corresponds to the star formation epoch considered in the ealaxy formation models of Blain Longair (1993b). | The upper bound $z_{dust}=20$ corresponds to the star formation epoch considered in the galaxy formation models of Blain Longair (1993b). |
We assume values for 0 similar to those implied. by observations of the space density of metal absorption systems from QSO spectra as a function of redshift (Sargent. Boksenberg Steidel 1988: Thomas Webster 1990). | We assume values for $\delta$ similar to those implied by observations of the space density of metal absorption systems from QSO spectra as a function of redshift (Sargent, Boksenberg Steidel 1988; Thomas Webster 1990). |
These systems are thought to arise in gas associated with galaxies and their haloes and it is quite plausible that such systems also contain dust. | These systems are thought to arise in gas associated with galaxies and their haloes and it is quite plausible that such systems also contain dust. |
Here we assume a direct proportionality between the amount of dust and heavy metal abundance in these systems. | Here we assume a direct proportionality between the amount of dust and heavy metal abundance in these systems. |
In ὃνgeneral. evolution in the number of metal absorption line systems per unit z. that takes into account effects. of cosmological expansion. can be parameterised: Evolution. such as a reduction in absorber numbers with redshift. can be interpreted. as either a decrease. in the comoving number density ni. or elfective cross-section πιο | In general, evolution in the number of metal absorption line systems per unit $z$, that takes into account effects of cosmological expansion, can be parameterised: Evolution, such as a reduction in absorber numbers with redshift, can be interpreted as either a decrease in the comoving number density $n_{z}$ , or effective cross-section $\pi r_{0}(z)^{2}$. |
With our assumption of a constant comoving density n(2)=no. and an evolving dust scale radius ry as defined by equation (9)). we have dNfdsx(1|z). where 520.5|28 for qa=0.5. | With our assumption of a constant comoving density $n(z)=n_{0}$, and an evolving dust scale radius $r_{0}$ as defined by equation \ref{rozev}) ), we have $dN/dz\propto(1+z)^{\gamma}$, where $\gamma=0.5+2\delta$ for $q_{0}=0.5$. |
Hence forevolution. ,= 0.5. | Hence for, $\gamma=0.5$ . |
Present estimates on the evolution of absorber numbers with redshift are poorly constrained. | Present estimates on the evolution of absorber numbers with redshift are poorly constrained. |
Thomas Webster (1990) have combined several datasets increasing absorption redshift ranges to give strong constraints on evolution mocels. | Thomas Webster (1990) have combined several datasets increasing absorption redshift ranges to give strong constraints on evolution models. |
For absorption (AA1548. 1551A)). which can be detected to redshifts ο,35 in high resolution opticalspectra. evolution has been confirmed for the highest. equivalent width svstems with Wy20.6A. | For absorption $\lambda\lambda$ 1548, ), which can be detected to redshifts $z\simgt3$ in high resolution opticalspectra, evolution has been confirmed for the highest equivalent width systems with $W_{0}\simgt0.6$. |
. It is more likely that these systems are those associated with dust rather than the lower equivalent width (presumably less chemically enriched) systems with uz0.3 which have a trend consistent with no evolution. | It is more likely that these systems are those associated with dust rather than the lower equivalent width (presumably less chemically enriched) systems with $W_{0}\simlt0.3$ which have a trend consistent with no evolution. |
Their value for the evolution parameter 5. for the highest equivalent width systems is 0.1d:0.5 at the 260 level. | Their value for the evolution parameter $\gamma$, for the highest equivalent width systems is $-0.1\pm0.5$ at the $2\sigma$ level. |
Converting this 20range to our model parameter ὃ using the discussion above. we assume the range: 0.5« | Converting this $2\sigma$range to our model parameter $\delta$ using the discussion above, we assume the range: $-0.5<\delta<-0.05$ . |
We can compare our assumed. ranges in evolutionary parameters: οnpn20 and 05«ὃ0.05 with recent determinations of the heavy element abundance in camped Ly-a absorption systems and the Ly-a forest to z~3. | We can compare our assumed ranges in evolutionary parameters: $6\leq z_{dust}\leq20$ and $-0.5<\delta<-0.05$ with recent determinations of the heavy element abundance in damped $\alpha$ absorption systems and the $\alpha$ forest to $z\sim3$. |
The dampec Ly-a systems are interpreted as the progenitors of galactic disks (Wolfe ct al. | The damped $\alpha$ systems are interpreted as the progenitors of galactic disks (Wolfe et al. |
1986). and recent studies by Pettini et al. ( | 1986), and recent studies by Pettini et al. ( |
1994: 1997). deduce metal abunclances and dust-to-gas ratios at zLS2.2 that are ~10% of the local value. | 1994; 1997) deduce metal abundances and dust-to-gas ratios at $z\sim1.8-2.2$ that are $\sim 10\%$ of the local value. |
The Lyman forest svstems however are more numerous. and usually correspond to gas columns 10° times lower than those of damped ντα absorbers. | The Lyman forest systems however are more numerous, and usually correspond to gas columns $>10^{7}$ times lower than those of damped $\alpha$ absorbers. |
Llieh resolution metal-line observations by Songaila (1997) deduce metallicities <=1.5% solar at 272.5XN. | High resolution metal-line observations by Songaila (1997) deduce metallicities $\simlt1.5\%$ solar at $z\sim2.5-3.8$. |
'To relate these metallicity estimates to cosmic evolution in dust content as specified by ourmodel. we must first note that the metallicity at any redshift Z(z). is generally defined as the mass fraction of heavy metals relativeto the total gasmass: Z(z)=GC)/ O0). | To relate these metallicity estimates to cosmic evolution in dust content as specified by ourmodel, we must first note that the metallicity at any redshift $Z(z)$ , is generally defined as the mass fraction of heavy metals relativeto the total gasmass: $Z(z)=\Omega_{m}(z)/\Omega_{g}(z)$ . |
At all redshifts. we assume a constant clust-to-metals ratio. €34(2)/,,(2). where a fixed fraction of heavy elements is assumed to be condensed into | At all redshifts, we assume a constant dust-to-metals ratio, $\Omega_{d}(z)/\Omega_{m}(z)$ , where a fixed fraction of heavy elements is assumed to be condensed into |
In principle. there is no need to observe spectrophotometric standards for deriving the extinction curve. as any relatively bright star could be used for this purpose. | In principle, there is no need to observe spectrophotometric standards for deriving the extinction curve, as any relatively bright star could be used for this purpose. |
However. observing standard stars has the advantage that the same data can be used also for the calibration plan purposes. hence mitigating the impact on normal science operations. | However, observing standard stars has the advantage that the same data can be used also for the calibration plan purposes, hence mitigating the impact on normal science operations. |
For this reason. the programme stars were chosen among those included in the FORSI calibration plan. | For this reason, the programme stars were chosen among those included in the FORS1 calibration plan. |
To limit the strength of the Balmer photospheric absorption lines (which tend to hamper the derivation of the extinction curve. especially in the blue domain). preference was given to hot. blue objects. | To limit the strength of the Balmer photospheric absorption lines (which tend to hamper the derivation of the extinction curve, especially in the blue domain), preference was given to hot, blue objects. |
The selected target stars are listed in Table 1.. which also presents their main properties. | The selected target stars are listed in Table \ref{tab:stars}, which also presents their main properties. |
Exposure times ranged from five seconds to a minute for the faintest targets Ge. GD50. BPM16274). | Exposure times ranged from five seconds to a minute for the faintest targets (i.e. GD50, BPM16274). |
Since the maximum shutter timing error across the whole field of view of FORSI is ~5 ms (Patat Romaniello 2005)). the photometric error associated to the exposure time uncertainty is or better. | Since the maximum shutter timing error across the whole field of view of FORS1 is $\sim$ 5 ms (Patat Romaniello \cite{shutter}) ), the photometric error associated to the exposure time uncertainty is or better. |
The spectroscopic data were collected on a time range spanning about 6 months. between October 4. 2008 and March 3]. 2009. | The spectroscopic data were collected on a time range spanning about 6 months, between October 4, 2008 and March 31, 2009. |
The target stars were observed randomly. mainly during morning twilight. | The target stars were observed randomly, mainly during morning twilight. |
On a few occasions the same star was observed several times during the same night. covering a wide range m airmass (hereafter indicated as X). | On a few occasions the same star was observed several times during the same night, covering a wide range in airmass (hereafter indicated as $X$ ). |
In total. more than 300 spectra were obtained for each of the two setups. with X. ranging from 1.0 to 2.6. | In total, more than 300 spectra were obtained for each of the two setups, with $X$ ranging from 1.0 to 2.6. |
The exact number of data points. time and airmass ranges are shown in Table 2.. together with the airmass distribution for each of the eight programme stars. | The exact number of data points, time and airmass ranges are shown in Table \ref{tab:log}, together with the airmass distribution for each of the eight programme stars. |
The observations were carried out under photometric or clear conditions. which were judged at the telescope based on the zero-points delivered by the available imaging instruments (transparency variations «105€ across the whole night in the V passband). | The observations were carried out under photometric or clear conditions, which were judged at the telescope based on the zero-points delivered by the available imaging instruments (transparency variations $<$ across the whole night in the $V$ passband). |
The quality of the nights was also checked a posteriori. using the data provided by the Line of Sight Sky Absorption Monitor (LOSSAM). which is part of the Differential Image Motion Monitor (DIMM) installed on Cerro Paranal (Sandrock et al. 2000)). | The quality of the nights was also checked a posteriori, using the data provided by the Line of Sight Sky Absorption Monitor (LOSSAM), which is part of the Differential Image Motion Monitor (DIMM) installed on Cerro Paranal (Sandrock et al. \cite{asm}) ). |
For this purpose. we have retrieved the DIMM archival data for all relevant nights. and examined the RMS fluctuation of the flux of the star used by the instrument to derive the prevailingseeing. | For this purpose, we have retrieved the DIMM archival data for all relevant nights, and examined the RMS fluctuation of the flux of the star used by the instrument to derive the prevailing. |
. When this fluctuation exceeded (or no LOSSAM data were available). the night was classified as non suitable. and the corresponding data | When this fluctuation exceeded (or no LOSSAM data were available), the night was classified as non suitable, and the corresponding data. |
jected.. Table 2. lists only data that passed this selection (600 out of 672 initial. non-saturated spectra). | Table \ref{tab:log} lists only data that passed this selection (600 out of 672 initial, non-saturated spectra). |
All spectra were obtained with the slit oriented along the N-S direction. which is strictly optimal only for observations close to the meridian. | All spectra were obtained with the slit oriented along the N-S direction, which is strictly optimal only for observations close to the meridian. |
The misalignment between the slit and the parallactic angle at large hour angles (rie. for targets at high airmass). can potentially lead to slit losses due to the differential atmospheric refraction (Filippenko1982)). and the seeing increase at larger zenith distances (Roddier 1981)). | The misalignment between the slit and the parallactic angle at large hour angles (i.e. for targets at high airmass), can potentially lead to slit losses due to the differential atmospheric refraction (Filippenko\cite{flipper}) ), and the seeing increase at larger zenith distances (Roddier \cite{roddier}) ). |
As a consequence. the estimated extinction coefficient might be systematically overestimated. | As a consequence, the estimated extinction coefficient might be systematically overestimated. |
To minimise this effect we used à 5 aresee wide slit for all observations: this. coupled to the typical seeing attained during our observations (see Table 3)). ensures that differential light losses are negligible for all data taken at X«2. | To minimise this effect we used a 5 arcsec wide slit for all observations; this, coupled to the typical seeing attained during our observations (see Table \ref{tab:seeing}) ), ensures that differential light losses are negligible for all data taken at $X<$ 2. |
Additionally. FORSI ts equipped with a Linear Atmospheric Dispersion Corrector (LADC). which is capable of maintaining the intrinsic image quality down to airmass ~ 1.5 (Avila. Rupprecht Becker 1997)). | Additionally, FORS1 is equipped with a Linear Atmospheric Dispersion Corrector (LADC), which is capable of maintaining the intrinsic image quality down to airmass $\sim$ 1.5 (Avila, Rupprecht Becker \cite{avila}) ). |
At larger airmasses the LADC only partially reduces the effect of the atmosphere. | At larger airmasses the LADC only partially reduces the effect of the atmosphere. |
The image quality values (FWHM) reported in Table 3 were deduced directly from the data. analysing the profiles perpendicular to the dispersion direction at different wavelengths. | The image quality values (FWHM) reported in Table \ref{tab:seeing}
were deduced directly from the data, analysing the profiles perpendicular to the dispersion direction at different wavelengths. |
The Table presents minimum (5,5). naximum (Sma) median (55,5) and 95-th percentile (sys) of the observed image quality distribution. | The Table presents minimum $s_{min}$ ), maximum $s_{max}$ ), median $s_{med}$ ) and 95-th percentile $s_{95}$ ) of the observed image quality distribution. |
The image quality turns out to be better than — 1.5 aresee in of the cases. | The image quality turns out to be better than $\sim$ 1.5 arcsec in of the cases. |
While we did not attempt to account for the effects of atmospheric refraction. we have applied a correction for the slit losses caused by seeing. | While we did not attempt to account for the effects of atmospheric refraction, we have applied a correction for the slit losses caused by seeing. |
The method is described in Appendix AppendixA:. | The method is described in Appendix \ref{sec:seeing}. |
. The data were processed using the FORS Pipeline (Izzo. de Bilbao Larsen 2009)). | The data were processed using the FORS Pipeline (Izzo, de Bilbao Larsen \cite{izzo}) ). |
The reduction steps include de-bias. flat-field correction. and 2D wavelength calibration. | The reduction steps include de-bias, flat-field correction, and 2D wavelength calibration. |
The spectra were then extracted non-interactively using the task in after optimizing the extraction parameters. | The spectra were then extracted non-interactively using the task in after optimizing the extraction parameters. |
Because of the wide (5 aresec) slit used to minimise flux losses. the uncertainty in the target positioning within. the. spectrograph entrance window Is expected to produce significant shifts in the wavelength solution. | Because of the wide (5 arcsec) slit used to minimise flux losses, the uncertainty in the target positioning within the spectrograph entrance window is expected to produce significant shifts in the wavelength solution. |
For this reason. for each standard star we selected a low-airmass template spectrum (drawn from the data sample). to which we applied a rigid shift in order to match O» and H»;O atmospheric absorptionbands?. | For this reason, for each standard star we selected a low-airmass template spectrum (drawn from the data sample), to which we applied a rigid shift in order to match $_2$ and $_2$ O atmospheric absorption. |
. Then. the shift to be applied to each input spectrum was computed via cross correlation to the corresponding template spectrum. | Then, the shift to be applied to each input spectrum was computed via cross correlation to the corresponding template spectrum. |
For doing this we first subtracted the smooth stellar continuum estimated by the task in IRAF. | For doing this we first subtracted the smooth stellar continuum estimated by the task in IRAF. |
Wavelength shifts exceeding | Wavelength shifts exceeding |
metallicitty and age can be determined from their primaries. | ty and age can be determined from theirwell-studied primaries. |
Nevertheless. during the last part of the observation. (he hard band light curve becomes erratic. probably caused by the hieh background. and does not track the soft band lieht CULVEe, | Nevertheless, during the last part of the observation, the hard band light curve becomes erratic, probably caused by the high background, and does not track the soft band light curve. |
Accorcingly. 85 OF1G+714 is much more variable in the soft than in the hard. N-ray band. | Accordingly, S5 0716+714 is much more variable in the soft than in the hard X-ray band. |
We use the factional variability amplitude(Fu... e.g.. Zhang οἱ al. | We use the factional variability amplitude, e.g., Zhang et al. |
1999) to quantily the sources variability. | 1999) to quantify the source's variability. |
In the 0.510 keV band. lis (25.2£1.6)%. | In the 0.5–10 keV band, is $25.2\pm1.6$. |
. In order to study the energy dependence of the variability amplitude. we calculate iin [ive (0.3 0.5.0.50.75. 0.75.1. 13 and 3.10 keV) energy bands. | In order to study the energy dependence of the variability amplitude, we calculate in five (0.3–0.5, 0.5–0.75, 0.75–1, 1–3 and 3–10 keV) energy bands. |
The results are tabulated in Table 4.. | The results are tabulated in Table \ref{tab:fvarlag}. |
In Figure 4... iis plotted against the photon energy. where the solid and open svibols indicate the results by excluding and including the high background interval. respectively. | In Figure \ref{fig:fvar}, is plotted against the photon energy, where the solid and open symbols indicate the results by excluding and including the high background interval, respectively. |
Except for the different values ofFi... the energy dependence of iis simular lor the (wo scenarios. | Except for the different values of, the energy dependence of is similar for the two scenarios. |
iincreases [from the 0.30.5 keV (o the 0.50.75 keV. then it decreases with higher energies. | increases from the 0.3–0.5 keV to the 0.5–0.75 keV, then it decreases with higher energies. |
In Figure 5.. we plot. from the top to bottom panels. the 0.3.10 keV light curve. and the temporal evolution of the 0.50.75 to 0.30.5 keV hardness ratios (representing the solt N-rav spectra) and the 310 t0 0.50.75 keV hardness ratios (representing the overall X-ray spectra). respectively. | In Figure \ref{fig:lchr}, we plot, from the top to bottom panels, the 0.3–10 keV light curve, and the temporal evolution of the 0.5–0.75 to 0.3–0.5 keV hardness ratios (representing the soft X-ray spectra) and the 3–10 to 0.5–0.75 keV hardness ratios (representing the overall X-ray spectra), respectively. |
The 0.50.75 to 0.30.5 keV ratios appear to follow the light curve. in the sense that the soft X-ray spectra flatten with increasing fluxes. | The 0.5–0.75 to 0.3–0.5 keV ratios appear to follow the light curve, in the sense that the soft X-ray spectra flatten with increasing fluxes. |
On the contrary. the 310 to 0.50.75 keV ratios seem (ο anti-correlate with the light curve. indicating that the overall spectra soften with increasing fluxes. | On the contrary, the 3–10 to 0.5–0.75 keV ratios seem to anti-correlate with the light curve, indicating that the overall spectra soften with increasing fluxes. |
The left plot of Figure G shows the relationship between the 0.50.75 to 0.30.5 keV ratios and the 0.510 keV count rates. | The left plot of Figure \ref{fig:loop} shows the relationship between the 0.5–0.75 to 0.3–0.5 keV ratios and the 0.5–10 keV count rates. |
Except for the data contaminated by the hieh backeround. the hardness ratios appear (o increase with higher count rates. showing the harder-when-brighter trend for the soft X-ray variations. | Except for the data contaminated by the high background, the hardness ratios appear to increase with higher count rates, showing the harder-when-brighter trend for the soft X-ray variations. |
The right plot of Figure G presents the relationship between the 310 to 0.50.75 keV ratios and the 0.510 keV count rates. | The right plot of Figure \ref{fig:loop} presents the relationship between the 3–10 to 0.5–0.75 keV ratios and the 0.5–10 keV count rates. |
lt is clear that the hardness ratios become smaller with higher count rates. indicating the softer-when-brighter phenomenon lor the overall X-ray. variations. | It is clear that the hardness ratios become smaller with higher count rates, indicating the softer-when-brighter phenomenon for the overall X-ray variations. |
Due to the long orbital period. iis able to. produce continuously sampled light curves over about one day. which is very important to study the inter-band time lags of the intra-day. X-ray. variability of blazars. | Due to the long orbital period, is able to produce continuously sampled light curves over about one day, which is very important to study the inter-band time lags of the intra-day X-ray variability of blazars. |
The lags can thus be estimated by calenlating the standard Cross-Correlation Function (CCF) between any (wo enerey band light curves. | The lags can thus be estimated by calculating the standard Cross-Correlation Function (CCF) between any two energy band light curves. |
We caleulate the CCFs between the 0.30.5 keV and the higher energv light curves. | We calculate the CCFs between the 0.3–0.5 keV and the higher energy light curves. |
The time interval affected by the high background. are excluded. | The time interval affected by the high background are excluded. |
Figure 7 plots the CCFs of the 0.30.5 keV with respect to the 0.50.75 and | Figure \ref{fig:ccf}
plots the CCFs of the 0.3–0.5 keV with respect to the 0.5–0.75 and |
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